 | W. P. Higgs - Algebra - 1876 - 122 pages
...divide by the first, to find the fourth term, or the answer. In arithmetic, too, we are told that " the mean proportional between two numbers is equal to the square root of their product." The reason we may perceive from the following proportion : a : b : : b : c Here b is what is termed... | |
 | Henry Bartlett Maglathlin - 1882 - 320 pages
...proportional between the extremes of a proportion is one of the equal means of the proportion (Art. 346), the mean proportional between two numbers is equal to the square root of their product. Hence, Л/816 X 97J = -v/79560 = 282.0638+, Ans. 75. r Ib. = 12 oz. ; 12 oz. : oz. = $- : x , Ans'... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...proportion a : b = b : c, we have 6* = ac, whence b = y^ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...proportion a : b = b : c, we have 6 2 == ac, whence b = y^ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6, Conversely, if the product of two numbers is equal to the product of two others, either two may... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...: с Let e : 6 :: b : c. Therefore I., ft2 = ac. Extract the square root, b = ^/a c. Hence, III. A mean proportional between two numbers is equal to the square root of their product. Let a:b::c:d. Therefore I., ad — be. ab Divide bv с d, - = -• с d IV. If four numbers are in... | |
 | John Henry Walsh - Arithmetic - 1893 - 392 pages
...12 inches, and the areas of their bases being 25 sq. in., 225 sq. in., and 75 sq. in., respectively. 12. Find the number of cubic feet in a block of stone...mean proportional between 64 and 196 is 8 x 14, or 112. Since each is multiplied by one-third of the altitude, the operation is shortened by adding together... | |
 | John Henry Walsh - 1893 - 426 pages
...each side of the lower base 5 feet. 1293. The volume of the frustum of a pyramid is equal to the Bum of the volumes of three pyramids, each having an altitude...mean proportional between 64 and 196 is 8 x 14, or 112. Since each is multiplied by one-third of the altitude, the operation is shortened by adding together... | |
 | Webster Wells - Arithmetic - 1893 - 382 pages
...square of the mean proportional between two numbers is equal to the product of the numbers. Hence, the mean proportional between two numbers is equal to the square root of their product. EXAMPLES. 270. 1. Find a fourth proportional to 7, 10, and 21." By Art. 268, the required fourth proportional... | |
 | William Chauvenet - 1893 - 340 pages
...the proportion a : b = b : c, we have & = ac, whence 6 = \/ac; that is, a mean proportional (II., 36) between two numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...: Ъ :: Ь : с. 4 Therefore I., l'¿ = nc. Extract the square root, Ъ = -у/а с. Hence, III. A mean proportional between two numbers is equal to the square root of their product. Let a : 6 : : с : d. Therefore I., ad = be. а Ъ Divide by с d, - = -5 • IV. If four numbers are,... | |
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V9 x 25 sq. ft. = 15 sq. ft. NOTE. — The mean proportional between two numbers is equal to the square root of their product. 13. Find the volume of the frustum of a square pyramid, its upper base containing 64 square inches, and its lower base 196 square... 
